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arXiv · 2402.19169

Improved bounds for skew corner-free sets

Adrian Beker
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Abstract

We construct skew corner-free subsets of $[n]^2$ of size $n^2\exp(-O(\sqrt{\log n}))$, thereby improving on recent bounds of the form $Ω(n^{5/4})$ obtained by Pohoata and Zakharov. In the other direction, we prove that any such set has size at most $O(n^2(\log n)^{-c})$ for some absolute constant $c > 0$. This improves on the previously best known upper bound, coming from Shkredov's work on the corners theorem.

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Adrian Beker. 2024-02-29. Improved bounds for skew corner-free sets. https://doi.org/10.1017/s0305004125000076

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